We illustrated the application of spatial regression models to examine the association between county-level racial/ethnic composition and reported cases of 2 STDs (chlamydia and gonorrhea), using Texas data for the year 2000. Our results imply that a unit change in percent black is associated with 1.6% (1.1% for Hispanic) and 3.3% (0.5% for Hispanic) change (on average) in chlamydia and gonorrhea rates respectively, compared with percent white. Thus while the average percent change in chlamydia rate associated with a unit change in percent black was slightly higher than the average percent change associated with a unit change in percent Hispanic (1.6% vs. 1.1%), the average percent change in gonorrhea rate associated with a unit change in percent black was substantially higher (3.3% vs. 0.5%)—over 6 times higher. Additionally, for percent black, the magnitude of the association is about 2 times higher for gonorrhea than for chlamydia (3.3% vs. 1.6%). In contrast, the magnitude of the association for percent Hispanic was about 2 times higher for chlamydia than for gonorrhea. The results confirmed the relatively higher association between percent black and STDs found in studies that accounted for spatial autocorrelation.12,13,37,38 However, none of them included percent Hispanic in their regression analyses so we cannot make any comparisons concerning the relative magnitude of association.
The control variables used in the analysis had the expected signs except the socio-economic variables. Their signs seemed counter-intuitive because higher rates of STDs are expected to be negatively associated with socio-economic status.10,52,53 However, at the county level, median household income was relatively high in the urban counties, which also tended to have higher STD rates. This may explain the positive association between STDs and median household income. On the other hand, percent owner-occupied had a negative association because urban counties with relatively higher STD rates had lower proportion of single-family homes, on average.
Although the spatial models (SAM and SEM) were superior (using standard criteria) it is important to point out that we did not find any substantial difference in the coefficients. Koumans et al13 did not provide information on alternative model comparisons with the spatial variable. Greenberg et al12 found substantial difference in the coefficients between the OLS and spatial model results using county-level gonorrhea data for 2002 in the United States. Delcher and Stover37 did not highlight the differences between the models they used. Semaan et al38 studied state-level association between social capital and STDs (gonorrhea and syphilis). Semaan et al38 also found no difference between OLS and spatial regression results when they controlled for population-level variables. Consequently, they suggested that the bulk of the spatial effect may have been captured by the racial composition variable, which may also explain our results. Thus spatial regression models may not always result in substantial changes in the coefficients of interest. However, they are superior methods and have become an indispensable part of regression analyses when, in theory, location plays an important part of the issue being studied, which is undeniably true for STDs.
We note limitations in the STD incidence data we used. The data were assembled from reported cases of infection which are dependent upon medical providers testing for primarily asymptomatic infections and providers or laboratory reporting positive results. Additionally, different localities may focus screening efforts on specific subpopulations thereby limiting the ability to generalize or extrapolate to the general population in any particular geographic unit. For instance, differences or similarities in how counties adhere to annual chlamydia screening for women in certain age groups recommended by individuals and national organizations54–58 may affect the county-level geographic distribution of the reported cases of chlamydia in this study. However, the extent to which it affects the results is difficult to assess. Also, the measure of percent Hispanic as reported by the 2000 census introduces some overlap in our measure of racial/ethnic composition as the Hispanic ethnic category includes other races.
Consensus on appropriate methods for adjusting rates to reduce variance instability and to make comparing rates from different locations more reliable has not been reached.59 Temporal smoothing is one method but may not be the best for STDs. However, for the purpose of identifying differences in STDs for counties in this study, it was a fairly robust measure because it provided an average over a 3-year period. More work is needed in this area to develop validated methods to reduce the “small-number problem” with incidence rates.
By focusing on only the counties within Texas, our analysis ignored spatial effects from counties that are contiguous to border counties but located in neighboring states. This omission may have affected our estimates, but it is difficult to determine the extent of the effect. This potential limitation, together with the problem of spatial heterogeneity illustrates the need for more studies to develop methods that use data from a relatively wider geographic area (such as all counties in the United States), while controlling for spatial autocorrelation and heterogeneity. Such methods would be useful to help understand the overall extent of the association between county-level racial/ethnic composition and STD rates.
This study has shown that, for the state of Texas, the exact specification of the spatial relationship (Queen or Rook) was important in measuring the extent of the spatial autocorrelation in STD rates. The difference was primarily because most counties in Texas were represented by “well-arranged” regular rectangular polygons. The difference may not exist with irregularly shaped or positioned polygons. Additionally, the exact reason for this difference may be understood from a contextual framework of local activities generating the signals from the existing data. In view of this, depending on the overall configuration of the polygons representing the spatial units of analyses, it is important to explore which specification gives the best results, because the exact type of spatial relationship used may be a source of statistically significant difference in the results obtained.32,36 The few studies that accounted for spatial autocorrelation in STD studies did not explore different spatial relationships and spatial regression models. Our study and previous studies have used larger geographic units (counties and states). Thus, further research is needed in this area, using smaller geographic units such as census blocks or cities, including more investigation into higher-order contiguity measures (i.e., spatial dependence that goes beyond the adjacent neighbors and accounts for the effects of the “neighbors of neighbors”).
Numerous previous studies have documented higher rates of reported STDs among certain minority racial/ethnic groups. Using county-level data on reported cases of chlamydia and gonorrhea for the state of Texas, we found that these disparities persisted at the county level even when controlling for STD rates in neighboring counties, although the association between county-level STD rates and racial/ethnic composition was dependent on the STD in question. In spite of the fact that there were no substantial differences in the magnitude of the estimated parameters, our illustrative analyses showed that the spatial regression models used were superior to the ordinary regression models and should be carefully explored in future studies.
1.Centers for Disease Control and Prevention. Sexually Transmitted Disease Surveillance, 2006. Atlanta, GA: Centers for Disease Control and Prevention, 2007.
2.Bakken IJ, Skjeldestad FE, Nordbo SA. Chlamydia trachomatis infections increase the risk for ectopic pregnancy: A population-based, nested case-control study. Sex Transm Dis 2007; 34:166–169.
3.Hillis SD, Joesoef R, Marchbanks PA, et al. Delayed care of pelvic inflammatory disease as risk factor for impaired fertility. Am J Obstet Gynecol 1993; 168:1503–1509.
4.Scholes D, Stergachis A, Heidrich FE, et al. Prevention of pelvic inflammatory disease by screening for cervical chlamydial infection. N Engl J Med 1996; 334:1362–1366.
5.Westrom L, Joesoef R, Reynolds G, et al. Pelvic inflammatory disease and fertility–a cohort study of 1,844 women with laparoscopically verified disease and 657 control women with normal laparoscopic results. Sex Transm Dis 1992; 19:185–192.
6.Geisler WM, Krieger JN. Epididymitis. In: Holmes KK, Sparling PF, Stamm WE, et al, eds. Sexually Transmitted Diseases. New York, NY: McGraw Hill, 2008:1127–1146.
7.Krieger JN. Prostatis syndrome: Causes, differential diagnosis, and clinical management. In: Holmes KK, Sparling PF, Stamm WE, et al, eds. Sexually Transmitted Diseases. New York, NY: McGraw Hill, 2008:1147–1174.
8.Martin DH. Urethritis in males. In: Holmes KK, Sparling PF, Stamm WE, et al, eds. Sexually Transmitted Diseases. New York, NY: McGraw Hill, 2008:1107–1126.
9.Adimora AA, Schoenbach VJ. Social context, sexual networks, and racial disparities in rates of sexually transmitted infections. J Infect Dis 2005; 191:S115–S122.
10.Aral SO. Understanding racial-ethnic and societal differentials in STI. Sex Transm Infect 2002; 78:2–4.
11.Farley TA. Sexually transmitted diseases in the southeastern united states: Location, race, and social context. Sex Transm Dis 2006; 33:S58–S64.
12.Greenberg ME, Koumans E, Swint E, et al. County-Level Characteristics Associated With Rates of Neiserria gonorrhoeae
in the United States, 2000 to 2002. Philadelphia, PA: National STD Prevention Conference; 2004.
13.Koumans EH, Sternberg M, Gwinn M, et al. Geographic variation of HIV infection in childbearing women with syphilis in the united states. AIDS 2000; 14:279–287.
14.Laumann EO, Youm Y. Racial/ethnic group differences in the prevalence of sexually transmitted diseases in the united states: A network explanation. Sex Transm Dis 1999; 26:250–261.
15.Zenilman JM. Ethnicity and sexually transmitted infections. Curr Opin Infect Dis 1998; 11:47–52.
16.Aral SO, Fullilove RE, Coutinho A, et al. Demographic and societal factors influencing risk behaviors. In: Wasserheit JN, Aral SO, Holmes KK, eds. Research Issues in Human Behavior and Sexually Transmitted Diseases in the AIDS Era. American Society for Microbiology 1992:161–175.
17.Becker KM, Glass GE, Brathwaite W, et al. Geographic epidemiology of gonorrhea in Baltimore, Maryland, using a geographic information system. Am J Epidemiol 1998; 147:709–716.
18.Bernstein KT, Curriero FC, Jennings JM, et al. Defining core gonorrhea transmission utilizing spatial data. Am J Epidemiol 2004; 160:51–58.
19.Bush KR, Henderson EA, Dunn J, et al. Mapping the core: Chlamydia and gonorrhea infections in Calgary, Alberta. Sex Transm Dis 2008; 35:291–297.
20.Ellen JM, Brown BA, Chung SE, et al. Impact of sexual networks on risk for gonorrhea and chlamydia among low-income urban African American adolescents. J Pediatr 2005; 146:518–522.
21.Ellen JM, Hessol NA, Kohn RP, et al. An investigation of geographic clustering of repeat cases of gonorrhea and chlamydial infection in San Francisco, 1989–1993: Evidence for core groups. J Infect Dis 1997; 175:1519–1522.
22.Elliott LJ, Blanchard JF, Beaudoin CM, et al. Geographical variations in the epidemiology of bacterial sexually transmitted infections in Manitoba, Canada. Sex Transm Infect 2002; 78:I139–I144.
23.Fox KK, Whittington WL, Levine WC, et al. Gonorrhea in the united states, 1981–1996–demographic and geographic trends. Sex Transm Dis 1998; 25:386–393.
24.Jennings JM, Curriero FC, Celentano D, et al. Geographic identification of high gonorrhea
transmission areas in Baltimore, Maryland. Am J Epidemiol 2005; 161:73–80.
25.Kerani RP, Handcock MS, Handsfield HH, et al. Comparative geographic concentrations of 4 sexually transmitted infections. Am J Public Health 2005; 95:324–330.
26.Law DCG, Serre ML, Christakos G, et al. Spatial analysis and mapping of sexually transmitted diseases to optimize intervention and prevention strategies. Sex Transm Infect 2004; 80:294–299.
27.Niccolai LM, Stephens N, Jenkins H, et al. Early syphilis among men in Connecticut: Epidemiologic and spatial patterns. Sex Transm Dis 2007; 34:183–187.
28.Webster LA, Rolfs RT, Nakashima AK, et al. Regional and temporal trends in the surveillance of syphilis, united states, 1986–1990. Morb Mortal Wkly Rep 1991; 40:29–33.
29.Wylie JL, Cabral T, Jolly AM. Identification of networks of sexually transmitted infection: A molecular, geographic, and social network analysis. J Infect Dis 2005; 191:899–906.
30.Zenilman JM, Ellish N, Fresia A, et al. The geography of sexual partnerships in Baltimore: Applications of core theory dynamics using a geographic information system. Sex Transm Dis 1999; 26:75–81.
31.Anselin L, Bera S. Spatial autocorrelation in linear regression models with an introduction to spatial econometrics. In: Ullah A, Giles DA, eds. Handbook of Applied Economic Statistics. New York, NY: Marcel Dekker, 1998.
33.Anselin L. Spatial Econometrics: Methods and Models. Boston, MA: Kluwer Academic Press, 1988.
34.Anselin L, Getis A. Spatial statistical-analysis and geographic information-systems. Ann Reg Sci 1992; 26:19–33.
35.Anselin L, Hudak S. Spatial econometrics in practice–a review of software options. Reg Sci Urban Econ 1992; 22:509–536.
36.Anselin L, Syabri I, Kho Y. Geoda: An introduction to spatial data analysis. Geogr Anal 2006; 38:5–22.
37.Delcher PC, Stover J. Geographic and spatial regression analysis of sexually transmitted diseases in Richmond, Virginia. Paper presented at: The 2006 National STD Prevention Conference; 2006; Jacksonville, FL.
38.Semaan S, Sternberg M, Zaidi A, et al. Social capital and rates of gonorrhea
and syphilis in the United States: Spatial regression analyses of state-level associations. Soc Sci Med 2007; 64:2324–2341.
39.Anselin L. Space and applied econometrics–introduction. Reg Sci Urban Econ 1992; 22:307–316.
41.Centers for Disease Control and Prevention. Sexually Transmitted Disease Surveillance, 2001. Atlanta, GA: Centers for Disease Control and Prevention, 2002.
42.Adimora AA, Schoenbach VJ. Contextual factors and the black-white disparity in heterosexual HIV transmission. Epidemiology 2002; 13:707–712.
44.LeSage JP, Pace RK. Spatial and spatiotemporal econometrics. Adv Econ 2004; 18:1–32.
45.Akaike H. Likelihood of a model and information criteria. J Econom 1981; 16:3–14.
46.Schwarz G. Estimating the dimension of a model. Ann Stat 1978; 6:461–464.
47.Belsley DA, Kuh E, Welsch RE. Regression Diagnostics. New York, NY: John Wiley & Sons, 1980.
48.Dicker LW, Mosure DJ, Berman SM, et al. Gonorrhea prevalence and coinfection with chlamydia in women in the United States, 2000. Sex Transm Dis 2003; 30:472–476.
49.Nsuami M, Cammarata CL, Brooks BN, et al. Chlamydia and gonorrhea co-occurrence in a high school population. Sex Transm Dis 2004; 31:424–427.
50.Zellner A. An efficient method for estimating seemingly unrelated regressions and tests of aggregation bias. J Am Stat Assoc 1962; 28:977–992.
51.Breusch T, Pagan A. A simple test for heteroskedasticity and random coefficient variation. Econometrica 1979; 47:1287–1294.
52.Adimora AA, Schoenbach VJ, Martinson FEA, et al. Social context of sexual relationships among rural African Americans. Sex Transm Dis 2001; 28:69–76.
53.Aral SO. Social and behavioral determinants of sexually transmitted disease: Scientific and technologic advances, demography, and the global political economy. Sex Transm Dis 2006; 33:698–702.
54.U.S. Preventive Services Task Force. Screening for chlamydial infection–recommendations and rationale. Am J Prev Med 2001; 20:90–94.
55.Centers for Disease Control and Prevention. Pelvic inflammatory disease: Guidelines for prevention and management. MMWR Recomm Rep 1991; 40:1–25.
56.Committee on Practice and Ambulatory Medicine. Recommendations for preventive pediatric health care. Pediatrics 1995; 96:373–374.
57.Elster AB, Kuznets NJ. Guidelines for Adolescent Preventive Services. Baltimore, MD: American Medical Association, 1994.
58.Hillis SD, Wasserheit JN. Screening for chlamydia–a key to the prevention of pelvic inflammatory disease. N Engl J Med 1996; 334:1399–1401.
59.Waller LA, Gotway CA. Applied Spatial Statistics for Public Health Data. Hoboken, NJ: John Wiley & Sons, 2004.
APPENDIX A. SPATIAL VARIABLES CREATED USING QUEEN AND ROOK CRITERIA
Carson county’s Queen contiguous (or first-order) neighbors are all eight counties that are contiguous to it - Moore, Hutchinson, Roberts, Potter, Gray, Randall, Armstrong, and Donley counties (see the zoomed insert in Fig. 1). Carson county’s Rook contiguous neighbors are Hutchinson, Potter, Gray, and Armstrong counties.
A nine-by-nine binary contiguity matrix for Queen and Rook neighbors based on the clipped insert in Figure 1 is presented below, where contiguous counties are assigned 1, or 0 otherwise.
Queen contiguity matrix:
Rook contiguity matrix:
The corresponding row-standardized (rows sum to unity) matrix is postmultiplied by the nine-by-one vector of the temporally smoothed rates. In matrix multiplication, each corresponding element in the resulting matrix is obtained by summing up the product of each row element in the first matrix and the corresponding column element in the second matrix.
i.e., WQueen · R = r
As an example, Carson county’s spatial lag (rC) created using the standardized Queen contiguity matrix gives:
Which is the average smoothed rate of all its 8 contiguous neighbors - Moore, Hutchinson, Roberts, Potter, Gray, Randall, Armstrong, and Donley.
i.e., WRook · R = r
By the same procedure, the spatial lag created using the standardized Rook contiguity matrix for Carson county gives:
Which is the average smoothed rates of its 4 contiguous neighbors with a common side - Hutchinson, Potter, Gray, and Armstrong. Cited Here...